Population Variance

Trying to put down why I think other animals are not as cultural as humans, I think it's important to go off on a little tangent about the importance of variation in traits within populations... It'll take me a little while to get to stuff I consider less appreciated (and therefore more interesting), so please bear with me.

Darwin formulated his theory of evolution while ignorant of genetics. Rather than the atomic inheritance model developed by Mendel and others, Darwin believed in blending inheritance - offspring would tend to be about halfway between each of their parents in any trait. I know R. A. Fisher pointed out that it is very difficult to reconcile blending inheritance with evolution (though I don't believe he was the first to make the point), because blending inheritance naturally reduces the variance of a trait in a population from generation to generation. In fact, I believe variance is supposed to be halved in each generation, when each child is thought to be the mathematical average of the parents. The existence of wide variation in nature, when coupled with blending inheritance, implied an impossible amount of adaptively more-or-less neutral mutation.

Hardy and Weinberg showed that this is not the case for Mendelian inheritance - for each generation reproducing by mixture of atomic genes, in a large enough population, with no selective advantage between genetic variants, and with a couple of other constraints, there will be no change in population variance in genes, or in the traits expressed by these genes. This equilibrium is actually a pretty strong force in a large number of species - in other words, the current gene pool has a lot of inertia, and evolutionary forces will generally act very slowly.

Let's take an example: Peter and Rosemary Grant were able to observe evolution occurring in Darwin's finches through two severe ecological changes - in one case, a drought, and in the other, a flood - and watched the distribution of beak sizes in the population change in response to both events - in the one case, the beaks became shorter and wider to crack open the tougher seeds during the drought, and then longer and narrower after the flood to more efficiently access the softer, smaller seeds that then became abundant. To give a sense of what may be happening evolutionarily, I'll construct a deliberately simplistic genetic model of beak shape: say there are four genes, each with two alleles, that determine the beak shape of a finch. For each gene, one of the alleles will cause the beak to be more stout, and the other will cause the beak to be more lean. We'll call the "stout" allele 0, and the "lean" allele 1, and overall beak shape is determined by how many "stout" and (by definition) "lean" alleles the organism possesses. Any individual in this population will then have K stout alleles, and 4-K lean alleles.

I've set this up to deliberately produce a binomial distribution of beak shapes (though there are complications even here - I note these complications in order to ignore them). In our model, we'll say that after the drought individuals with 3 stout alleles and 1 lean allele will have the optimal beak shape; after the flood, individuals with 3 lean alleles and 1 stout allele will have optimal beak morphology. In neither case should any allele be completely eliminated from the population, which means that there will always be the potential to adapt to the flood after a drought, and to the drought after the flood.

This leads directly to what I think is the core of why culture is not nearly so intensely used in non-human animals as it is in humans: cultural evolution includes a lot of blending of received information, blending inheritance reduces population variance, and reduced variance lowers the ability to respond to ecological change. I may unpack this more later...